chevron icon chevron icon chevron icon

Fractions - Addition & Subtraction

In this article, we will learn more about Addition and Subtraction of Fractions in \(\text{P5}\) level.  We will also be solving simple word problems involving addition and subtraction.

The learning objectives are:

  1. Relating fractions and division
  2. Addition of mixed numbers 
  3. Subtraction of mixed numbers 
  4. Simple word problems involving addition and subtraction of mixed numbers

1. Relating Fractions And Division

Fraction is related to division. 

\(\begin{align*} \frac {1} {3} \end{align*}\) is the same as \(\begin{align*} 1 \div 3 \end{align*}\).

 

Question 1: 

Express each of the following as a fraction. 

A. \(3 \div 5 =\text{__________}\)

B. \(5 \div 9 = \text{__________}\)

C. \(6 \div 11 = \text{__________}\)

Solution: 

A. \(\displaystyle{3 \div 5 =\frac {3}{5}}\)

B. \(\displaystyle{5 \div 9 = \frac {5}{9}}\)

C. \(\displaystyle{ 6 \div 11 = \frac {6}{11} }\)

 

Question 2: 

Mary bought \(2\) pies. She divided it equally among her \(3\) children. What fraction of a pie did each child receive?

Solution: 

Fraction of a pie each child received  \(\displaystyle{=2 \div 3\\[2ex] = \frac {2}{3} }\)

Answer:

\(\begin{align*} \frac {2}{3} \end{align*}\)

 

Question 3:

Jack baked \(15\) muffins and shared them equally with \(6\) friends. What fraction of the muffins did each of them receive?

Solution: 

Total muffins baked \(= 15\) muffins

Total number of friends including Jack \(= 7\)

15 muffins are shared \(\text{equally}\) among \(7 \text{ people}\).

Method 1:

Fraction of muffins received by each friend \(\displaystyle{= 15 \div 7\\[2ex] = \frac{15}{7}\\[3ex] = 2\frac{1}{7}\\[3ex]}\)        

Method 2:

\(\require{enclose} \begin{array}{rll} 0 \;2\phantom{000} \\[-3pt] 7\; \enclose{longdiv}{1\;5\quad}\kern-.3ex \\[-3pt] \underline{^-0\phantom{000}} \\[-3pt] 1\;5 \phantom{00} \\[-3pt] \underline{^-\text{1 4}\quad}\phantom{} \\[-3pt] 1 \phantom{00} \\[-3pt] \end{array}\)

Answer:

\(\begin{align*} 2 \frac {1}{7} \end{align*}\)

 

2. Addition Of Mixed Numbers 

To do addition of mixed numbers, we do the following steps:

Step 1:

Add the whole numbers.

Step 2:

Ensure that the denominators are the same. Make the denominators the same if they are not.

Step 3:

Add the fractions. 

Step 4:

Simplify and express as a mixed number if possible. 

 

Question 1: 

Add the following.

\(\begin{align*} 2\frac { 2} { 5} + 5\frac {1 } {5 } \end{align*}\)

Solution: 

\(\begin{align*} 2\frac { 2} { 5} + 5\frac {1 } {5 } &= 7\frac { 2} { 5} + \frac {1 } {5 }\\ \\ &= 7\frac { 3} { 5} \\ \end{align*}\)

 

Question 2: 

Add the following.

\(\begin{align*} 1\frac {7} {10} + 6\frac {9} {10} \end{align*}\)

Solution: 

\(\begin{align*} 1\frac { 7} { 10} + 6\frac {9 } {10 } &= 7\frac { 7} { 10} + \frac {9 } {10 }\\ \\ &= 7\frac { 16} { 10} \\ \\ &= 8\frac { 6} { 10} \\ \\ &= 8\frac { 3} { 5} \\ \end{align*}\)

Answer:

\(\begin{align*} 8\frac { 3} { 5} \end{align*}\)

 

Question 3: 

Add the following.

\(\begin{align*} 2\frac {3} {4} + 3\frac {5} {6} \end{align*}\)

Solution: 

\(\begin{align*} 2\frac { 3} { 4} + 3\frac {5 } {6} &= 5\frac { 3} { 4} + \frac {5 } {6 }\\ \\ &= 5\frac { 9} { 12} + \frac {10 } {12 }\\ \\ &= 5\frac { 19} { 12} \\ \\ &= 6\frac { 7} { 12} \\ \end{align*} \)
 

Answer:

\(\begin{align*} 6\frac { 7} { 12} \end{align*}\)

 

Question 4: 

Add the following.

\(\begin{align*} 1\frac {6} {7} + 5\frac {9} {14} \end{align*}\)

Solution: 

\(\begin{align*} 1\frac { 6} { 7} + 5\frac {9 } {14} &= 6\frac { 6} { 7} + \frac {9 } {14 }\\ \\ &= 6\frac { 12} { 14} + \frac { 9} { 14}\\ \\ &= 6\frac { 21} { 14} \\ \\ &= 7\frac { 7} { 14} \\ \\ &= 7\frac { 1} { 2} \\ \end{align*}\)

Answer:

\(\begin{align*} 7\frac { 1} { 2} \end{align*}\)

 

3. Subtraction Of Mixed Numbers

To do addition of mixed numbers, we do the following steps:

Step 1:

Subtract the whole numbers.

Step 2:

Ensure that the denominators are the same. Make the denominators the same if they are not.

Step 3:

Rename the first mixed number if the numerators cannot be subtracted.

Step 4:

Subtract the fractions.

Step 5:

Simplify and express as a mixed number if possible.

 

Question 1: 

Subtract the following. 

\(\begin{align*} 5\frac {5} {6} - 1\frac {1} {3} \end{align*}\)

Solution: 

\(\begin{align*} 5\frac {5} {6} - 1\frac {1} {3} &= 4\frac { 5} { 6} - \frac {1 } {3 }\\ \\ &= 4\frac { 5} { 6} - \frac {2 } {6 }\\ \\ &= 4\frac { 3} { 6} \\ \\ &= 4\frac { 1} { 2} \\ \end{align*}\)

Answer:

\(\begin{align*} 4\frac { 1} { 2} \end{align*}\)

 

Question 2: 

Subtract the following.

\(\begin{align*} 7\frac {3} {8} - 6\frac {7} {8} \end{align*}\)

Solution: 

\(\begin{align*} 7\frac {3} {8} - 6\frac {7} {8} &= 1\frac { 3} { 8} - \frac {7 } {8 }\\ \\ &= \frac { 11} { 8} - \frac {7 } {8 }\\ \\ &= \frac { 4} { 8} \\ \\ &= \frac { 1} { 2} \\ \end{align*}\)

Alternatively, convert both fractions to improper fractions.

\(\begin{align*} 7\frac {3} {8} - 6\frac {7} {8} &= \frac { 59} { 8} - \frac {55} {8 }\\ \\ &= \frac { 4} { 8} \\ \\ &= \frac { 1} { 2} \\ \end{align*}\)

Answer:

\(\begin{align*} \frac {1} {2} \end{align*}\)

 

Question 3: 

Subtract the following.

\(\begin{align*} 6\frac {3} {10} - 1\frac {1} {2} \end{align*}\)

Solution: 

\(\begin{align*} 6\frac {3} {10} - 1\frac {1} {2} &= 5\frac { 3} { 10} - \frac {1} {2}\\ \\ &= 5\frac { 3} { 10} - \frac {5} {10} \\ \\ &= 4\frac { 13} { 10} - \frac {5} {10} \\ \\ &= 4\frac { 8} { 10} \\ \\ &= 4\frac { 4} { 5} \\ \end{align*}\)

Alternatively, convert both fractions to improper fractions.

\(\begin{align*} 6\frac {3} {10} - 1\frac {1} {2} &= \frac { 63} { 10} - \frac {3} {2} \\[3ex] &= \frac { 63} { 10} - \frac {15} {10} \\[3ex] &= \frac {48} { 10} \\[3ex] &= 4\frac { 8} { 10} \\[3ex] &= 4\frac { 4} { 5} \end{align*}\)

Answer:

\(\begin{align*} 4\frac { 4} { 5} \end{align*}\)

 

Question 4: 

Subtract the following.

\(\begin{align*} 5\frac {7} {10} - 3\frac {3} {4} \end{align*}\)

Solution: 

\(\begin{align*} 5\frac { 7 } { 10 } - 3 \frac { 3 } { 4 } &= 2 \frac { 7 } { 10 } - \frac { 3 } { 4 }\\ \\ &= 2 \frac { 14 } { 20 } - \frac { 15 } { 10 } \\ \\ &= 1 \frac { 34 } { 20 } - \frac { 15 } { 10 }\\ \\ &= 1\frac { 19 } { 20 } \\ \end{align*}\)

Answer:

\(\begin{align*} 1\frac { 19 } { 20 } \end{align*}\)

 

4. Word Problems Involving Addition And/or Subtraction Of Mixed Numbers

Question 1: 

Jane had \(\begin{align*} 2\frac { 3 } { 5 }\; \text {kg} \end{align*}\) of coffee powder. Sarah has \(\begin{align*} 1\frac { 1 } { 5 } \; \text {kg} \end{align*}\) of coffee powder more than Jane. How much coffee powder does Sarah have?

Solution: 

Mass of coffee powder Sarah has \(\displaystyle{= 2 \frac { 3 } { 5 } \; \text {kg} + 1\frac { 1 } { 5 } \;\text {kg}\\[3ex] = 3 \frac { 4 } { 5 } \; \text {kg}}\)

Answer:

\(\begin{align*} 3 \frac { 4 } { 5 } \; \text {kg} \end{align*}\)

 

Question 2: 

Mrs Tan had \(\begin{align*} 5\frac { 1 } { 2 }\; \text {kg} \end{align*}\) of flour. She had \(\begin{align*} 2\frac { 5 } { 6 }\; \text {kg} \end{align*}\) of flour more than Mrs Loh. How much flour did they have altogether?

Solution: 

Mass of flour Mrs Loh had \(\displaystyle{= 5\frac { 1 } { 2 }\; \text {kg} - 2\frac { 5 } { 6 }\; \text {kg}\\[3ex] = 3\frac { 1 } { 2 }\; \text {kg} - \frac { 5 } { 6 }\; \text {kg} \\[3ex] = 3\frac { 3 } { 6 }\; \text {kg} - \frac { 5 } { 6 }\; \text {kg} \\[3ex] = 2\frac { 9 } { 6 }\; \text {kg} - \frac { 5 } { 6 }\; \text {kg} \\[3ex] = 2\frac { 4 } { 6 }\; \text {kg} \\[3ex] = 2\frac { 2 } { 3 }\; \text {kg}}\)  

Total mass of flour they had \(\displaystyle{= 5\frac { 1 } { 2 }\; \text {kg} + 2\frac { 2 } { 3 }\; \text {kg} \\[3ex] = 7\frac { 1 } { 2 }\; \text {kg} + \frac { 2 } { 3 }\; \text {kg} \\[3ex] = 7\frac { 3 } { 6 }\; \text {kg} + \frac { 4 } { 6 }\; \text {kg} \\[3ex] = 7\frac { 7 } { 6 }\; \text {kg} \\[3ex] = 8\frac { 1 } { 6 }\; \text {kg}}\)

Answer:

\(\begin{align*} 8\frac { 1 } { 6 }\; \text {kg} \end{align*}\)

 

Question 3:

Sandy had \(\begin{align*} 3\frac { 1 } { 2 }\; \text {kg} \end{align*}\) of sugar. She had \(\begin{align*} 2\frac { 5 } { 6 }\; \text {kg} \end{align*}\) of sugar less than Amy. How many kilograms of sugar did they have altogether?

Solution: 

Mass of sugar Amy had \(\displaystyle{= 3\frac { 1 } { 2 }\; \text {kg} + 2\frac { 5 } { 6 }\; \text {kg} \\[3ex] = 5\frac { 1 } { 2 }\; \text {kg} + \frac { 5 } { 6 }\; \text {kg} \\[3ex] = 5\frac { 3 } { 6 }\; \text {kg} + \frac { 5 } { 6 }\; \text {kg} \\[3ex] = 5\frac { 8 } { 6 }\; \text {kg} \\[3ex] = 6\frac { 2 } { 6 }\; \text {kg} \\[3ex] = 6\frac { 1 } { 3 }\; \text {kg}}\)

Total mass of sugar Sandy and Amy had \(\displaystyle{= 3\frac { 1 } { 2 }\; \text {kg} + 6\frac { 1 } { 3 }\; \text {kg} \\[3ex] = 9\frac { 1 } { 2 }\; \text {kg} + \frac { 1 } { 3 }\; \text {kg} \\[3ex] = 9\frac { 3 } { 6 }\; \text {kg} + \frac { 2 } { 6 }\; \text {kg} \\[3ex] = 9\frac { 5 } { 6 }\; \text {kg}}\)

Answer:

\(\begin{align*} 9\frac { 5 } { 6 }\; \text {kg} \end{align*}\)

 

Conclusion

In this article, we have learnt about Addition and Subtraction of Fractions as per the Primary 5 Math level. We have learnt the following subtopics in fractions.

  • Relating fractions and division
  • Addition of mixed numbers 
  • Subtraction of mixed numbers 
  • Simple word problems involving addition and subtraction of mixed numbers

 


 

Continue Learning
Volume Of A Liquid Decimals - Operations & Conversions
Ratio: Introduction Average - Formula
Percentage, Fractions And Decimals Whole Numbers
Strategy - Equal Stage Angle Properties
Table Rates Whole Number Strategy: Gap & Difference
Fractions - Addition & Subtraction Ratio Strategy: Repeated Identity

 

Resources - Academic Topics
icon expand icon collapse Primary
icon expand icon collapse Secondary
icon expand icon collapse
Book a free product demo
Suitable for primary & secondary
select dropdown icon
Our Education Consultants will get in touch with you to offer your child a complimentary Strength Analysis.
Book a free product demo
Suitable for primary & secondary
Claim your free demo today!
Claim your free demo today!
Arrow Down Arrow Down
Arrow Down Arrow Down
*By submitting your phone number, we have your permission to contact you regarding Geniebook. See our Privacy Policy.
Geniebook CTA Illustration Geniebook CTA Illustration
Turn your child's weaknesses into strengths
Geniebook CTA Illustration Geniebook CTA Illustration
Geniebook CTA Illustration
Turn your child's weaknesses into strengths
Get a free diagnostic report of your child’s strengths & weaknesses!
Arrow Down Arrow Down
Arrow Down Arrow Down
Error
Oops! Something went wrong.
Let’s refresh the page!
Error
Oops! Something went wrong.
Let’s refresh the page!
We got your request!
A consultant will be contacting you in the next few days to schedule a demo!
*By submitting your phone number, we have your permission to contact you regarding Geniebook. See our Privacy Policy.
1 in 2 Geniebook students scored AL 1 to AL 3 for PSLE
Trusted by over 220,000 students.
Trusted by over 220,000 students.
Arrow Down Arrow Down
Arrow Down Arrow Down
Error
Oops! Something went wrong.
Let’s refresh the page!
Error
Oops! Something went wrong.
Let’s refresh the page!
We got your request!
A consultant will be contacting you in the next few days to schedule a demo!
*By submitting your phone number, we have your permission to contact you regarding Geniebook. See our Privacy Policy.
media logo
Geniebook CTA Illustration
Geniebook CTA Illustration
Geniebook CTA Illustration
Geniebook CTA Illustration Geniebook CTA Illustration
icon close
Default Wrong Input
Get instant access to
our educational content
Start practising and learning.
No Error
arrow down arrow down
No Error
*By submitting your phone number, we have
your permission to contact you regarding
Geniebook. See our Privacy Policy.
Success
Let’s get learning!
Download our educational
resources now.
icon close
Error
Error
Oops! Something went wrong.
Let’s refresh the page!